Simplify the following expression: $5\sqrt{63}$.
Solution: First, try to factor a perfect square out of the radical. $= 5\sqrt{63}$ $= 5\sqrt{9 \cdot 7}$ Separate the radical and simplify. $= 5\sqrt{9} \cdot \sqrt{7}$ $= 5 \cdot 3 \cdot \sqrt{7}$ $= 15\sqrt{7}$